The bolded inequalities correspond to curves \(C\)  with \(\mathcal {N}_C\)  not of type \((-1,-1)\) . We know by [1]} that the other inequalities are necessary and define Type I walls of \(\mathfrak {C}_0\) . The inequalities from divisors parameterising rigid subsheaves are
\(  \theta _1>0, \\  \theta _7>0, \\  \theta _{11}>0, \\  \theta _{13}>0, \\  \theta _{14}>0, \\  \theta _{16}>0, \\  \theta _{17}>0, \\  \theta _{19}>0, \\  \theta _{21}>0, \\  \theta _{22}>0, \\  \theta _{23}>0, \\  \theta _{26}>0, \\  \theta _{29}>0.\qquad \mathrm {(A_1,A_7,A_{11},A_{13},A_{14},A_{16},A_{17},A_{19},A_{21},A_{22},A_{23},A_{26},A_{29})}\) 
